A periodic first principle study to design microporous crystal 12MO, 7Al2O3 for selective and active O radicals encaging

Periodic first principle calculation correlates the role of metal substitution (Sr and Ba in place of Ca) on selective encaging of active O⁻ radicals inside the microporous 12MO, 7Al₂O₃ crystal structure. We have exchanged Ca by Sr and Ba and as well extracted electron stepwise to monitor selectivity of different anion encaging inside the same structure type. Ca favors O²⁻ encaging and shows no electron transition when neutral, whereas Sr shows no transition in absence of unpaired electron and can successfully trap O⁻, Ba though less active than the other metal substituents shows oxygen encaging at its zero and mono-positive state.     

Atomic one- and two-electron subshell moments in position and momentum spaces

For 357 subshells of the 53 neutral atoms He through Xe in their ground states, the two-electron intracule (relative motion) <u ^k > _nl and extracule (center-of-mass motion) <R ^k > _nl subshell moments in position space are examined as well as their counterparts <v ^k > _nl and <P ^k > _nl in momentum space, where n and l are the principal and azimuthal quantum numbers of the atomic subshell, respectively. It is clarified that between the intracule and extracule moments the “2 ^k -rule” is strictly valid, which means <u ^k > _nl = 2 ^k <R ^k > _nl and <v ^k > _nl = 2 ^k <P ^k > _nl for any nl subshell. Theoretical analysis also proves that for a particular case of k = +2, two relations <u ²> _nl = (N _nl −1)<r ²> _nl and <v ²> _nl = (N _nl −1)<p ²> _nl hold exactly, where N _nl (≥2) is the number of electrons in the subshell nl, and <r ^k > _nl and <p ^k > _nl are the familiar one-electron subshell moments in position and momentum spaces, respectively. The latter equality establishes a new and rigorous relation between the second electron-pair moments in momentum space and the total energy of an atom through the virial theorem. For k=+1, −1, and −2, the numerical Hartree-Fock results for the 357 subshells show that there are approximate but accurate linear relations between <u ^k > _nl and <r ^k > _nl and between <v ^k > _nl and <p ^k > _nl , in which the proportionality constant in each space depends on n,l, and k. Received: 27 April 1998 / Accepted: 29 May 1998 / Published online: 28 August 1998     

Metalloporphyrin Cr(TPP)Cl-catalyzed Claisen rearrangement of simple aliphatic allyl vinyl ethers and its unique stereoselectivity

The catalytic Z-selective Claisen rearrangement of simple aliphatic allyl vinyl ethers can be achieved using a chromium(III) porphyrin complex, Cr(TPP)Cl, as a catalyst: Cr(TPP)Cl significantly enhances reversal of E-Z selectivity in the thermal Claisen rearrangement of allyl vinyl ethers, especially, 4,5- and 4,6-disubstituted derivatives, at low catalyst loading.     

Relativistic correlating basis sets for 57La and 89Ac

Developed and reported are compact yet efficient correlating basis sets for the ₅₇La and ₈₉Ac atoms, missing in the literature. Good performance of these correlating sets is exemplified in molecular applications to diatomic oxides and fluorides. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Interference, fluctuation, and alternation of electron tunneling in protein media. 2. Non-condon theory for the energy gap dependence of electron transfer rate

Developing the quantum transition rate theory of Prezhdo and Rossky (J. Chem. Phys. 1997, 107, 5863), we produced a new non-Condon theory of the rate of electron transfer (ET) which happens through a protein medium with conformational fluctuation. The new theory is expressed by a convolution form of the power spectrum for the autocorrelation function of the electronic tunneling matrix element T(DA)(t) with quantum correction and the ordinary Franck-Condon factor. The new theory satisfies the detailed balance condition for the forward and backward ET rates. The ET rate formula is divided into two terms of elastic and inelastic tunneling mechanisms on the mathematical basis. The present theory is applied to the ET from Bph(-) to Q(A) in the reaction center of Rhodobacter sphaeroides. Numerical calculations of T(DA)(t) were made by a combined method of molecular dynamics simulations and quantum chemistry calculations. We showed that the normalized autocorrelation function of T(DA)(t) is almost expressed by exponential forms. The calculated energy gap law of the ET rate is nearly Marcus' parabola in most of the normal region and around the maximum region, but it does not decay substantially in the inverted region, which is called the anomalous inverted region. We also showed that the energy gap law at the high uphill energy gap in the normal region is elevated considerably from the Marcus' parabola, which is called the anomalous normal region. Those anomalous energy gap laws are due to the inelastic tunneling mechanism which works actively at the energy gap far from zero. We presented an empirical formula for easily calculating the non-Condon ET rate, which is usable by many researchers. We provided experimental evidence for the anomalous inverted region which was basically reproduced by the present theory. The present theory was extensively compared with the previous non-Condon theories.     

Atomic electron-pair distances and subshell radii in position and momentum space

For the 53 neutral atoms from He to Xe in their ground states, the average distances < u> _{n l , n ′ l ′} in position space and < v> _{n l , n ′ l ′} in momentum space between an electron in a subshell nl and another electron in a subshell n ^′ l ^′ are studied, where n and l are the principal and azimuthal quantum numbers of an atomic subshell, respectively. Analysis of 1700 subshell pairs shows that the electron-pair distances < u> _{n l , n ′ l ′} in position space have an empirical but very accurate linear correlation with a one-electron quantity U _{n l , n ′ l ′}≡L _r +S _r ²/(3L _r ), where L _r and S _r are the larger and smaller of subshell radii < r> _{n l} and < r> _{n ′ l ′}, respectively. The correlation coefficients are never smaller than 0.999 for the 66 different combinations of two subshells appearing in the 53 atoms. The same is also true in momentum space, and the electron-pair momentum distances < > _{n l , n ′ l ′} have an accurate linear correlation with a one-electron momentum quantity V _{n l , n ′ l ′}≡L _p +S _p ²/(3L _p ), where L _p and S _p are the larger and smaller of average subshell momenta < p> _{n l} and < p> _{n ′ l ′}, respectively. Trends in the proportionality constants between < u> _{n l , n ′ l ′} and U _{n l , n ′ l ′} and between < > _{n l , n ′ l ′} and V _{n l , n ′ l ′} are discussed based on a hydrogenic model for the subshell radial functions. Received: 8 April 1998 / Accepted: 6 July 1998 / Published online: 18 September 1998     

Charge and radial correlations in helium and helium-like atoms

Summary For two-electron atoms, the method of a variable exponent, which treats the orbital exponent (or effective nuclear charge) of an electron as an explicit function of the radial coordinate of the other electron, is studied. The method is shown to improve the energy and other electronic properties remarkably. An incorporation of the variable exponent into the Kellner approximation for He, for example, gives the energy –2.872 606 1 a.u., which is lower than the original Kellner energy by 0.024 949 8 a.u. and exceeds the Hartree-Fock limit energy by 0.010 926 1 a.u. The improvement due to the variable exponent originates from the inclusion of the charge and radial correlations. Applications of the method to the Eckart and Hylleraas approximations are also presented.     

Marginal electron density and density-difference functions

Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y ₀,z ₀) and the two-dimensional cut (x, y, z ₀) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions _x (x) and _xy (x, y) and their difference functions _x (x) and _xy (x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H₂ system.